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Contract No. DE-AC36-08GO28308

Representation of Solar Capacity 

Value in the ReEDS Capacity 

Expansion Model

B. Sigrin, P. Sullivan, E. Ibanez, and R. Margolis

Technical Report

NREL/TP-6A20-61182

March 2014
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

Representation of Solar Capacity 

Value in the ReEDS Capacity 

Expansion Model

B.Sigrin, P. Sullivan, E. Ibanez, and R. Margolis

Prepared under Task No. SS13.1020

Technical Report

NREL/TP-6A20-61182

March 2014
NOTICE

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Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 

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Printed on paper containing at least 50% wastepaper, including 10% post-consumer waste.
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Acknowledgments

This project was funded by the U.S. Department of Energy Solar Energy Technologies Program. 

We thank Paul Denholm, Seyed Madaeni, Kelly Eurek, Jennie Jorgenson, and Trieu Mai for 

input and assistance on this project. Opinions represented in this article are the authors’ own and 

do not reflect the view of the U.S. Department of Energy or the U.S. Government. This work was 

supported by the U.S. Department of Energy under contract number DE-AC36-08GO28308. 
iv

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List of Acronyms

APS Arizona Public Service

BA balancing area

CSP concentrating solar power

DOE U.S. Department of Energy

DUPV distributed utility-scale photovoltaics

EFOR effective forced outage rate

ELCC effective load-carrying capacity

ISO Independent System Operator

IVGTF Integration of Variable Generation Task Force

LOLE loss of load expectation

LOLP loss of load probability

NERC North American Electric Reliability Corporation

NREL National Renewable Energy Laboratory

PSCo Public Service of Colorado

PV photovoltaic(s)

ReEDS Regional Energy Deployment System

REPRA Renewable Energy Probabilistic Resource 

Adequacy

SAM System Advisor Model

TEPPC Transmission Expansion Planning Policy 

Committee

TriState TriState Generation and Transmission

UPV utility-scale photovoltaics

VRRE variable resource renewable energy

WECC Western Electricity Coordinating Council

WWSIS-2 Western Wind and Solar Integration Study Phase 2
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Executive Summary

An important emerging issue for electricity system operators is the estimation of renewables’ 

contributions to reliably meeting system demand, or their capacity value. While the capacity 

value of thermal generation can be estimated easily, assessment of wind and solar requires a 

more nuanced approach due to resource variability. Reliability-based methods, particularly 

assessment of the effective load-carrying capacity (ELCC), are considered to be the most robust 

and widely accepted techniques for addressing this resource variability. 

This report validates treatment of solar photovoltaic (PV) capacity value by the Regional Energy 

Deployment System (ReEDS) capacity expansion model by comparing model results against two 

sources. The first comparison is against values published by utilities or other entities for known 

electrical systems at existing solar penetration levels. The second comparison is against a timeseries ELCC simulation tool for high renewable penetration scenarios in the Western 

Interconnection. Results from the ReEDS model are found to compare well with both 

comparisons--despite not being resolved at an hourly scale.

Two results are relevant for other capacity-based models that do not use hourly calculations to 

model solar capacity value. First, solar capacity value should not be parameterized as a static 

value but must decay with increasing penetration. This is because, for an afternoon-peaking 

system, as solar penetration increases the system’s peak net load shifts to later in the day-- when 

solar output is lower. Second, long-term planning models should determine how system 

adequacy requirements differ between time periods in order to approximate loss of load 

probability (LOLP) calculations. Within the ReEDS model we resolve these issues by using a 

capacity value estimate that varies by time-slice. Within each time-slice the net load and shadow 

price on ReEDS’s planning reserve constraint signals the relative importance of additional firm 

capacity.
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Table of Contents

List of Figures ........................................................................................................................................... vii

List of Tables ............................................................................................................................................. vii

1 Introduction........................................................................................................................................... 1

1.1 Report Outline.................................................................................................................................. 2

2 Factors Influencing Modeled Capacity Value .................................................................................... 2

2.1 Sensitivity of Capacity Value to Resource Quality ......................................................................... 2

2.1.1 Correlation of Load and Solar Generation........................................................................ 3

2.2 Solar Energy Penetration ................................................................................................................. 3

3 ReEDS Background.............................................................................................................................. 5

3.1 Model Structure ............................................................................................................................... 5

3.2 Capacity Value Calculations............................................................................................................ 7

3.2.1 Capacity Value Point Estimates........................................................................................ 7

3.2.2 Benefits of Power Diversification..................................................................................... 9

4 Comparison of Capacity Value at Low Penetration ........................................................................ 10

4.1 Estimates of Solar Capacity Credit in Planning Studies and Similar Literature............................ 10

4.2 ReEDS Scenario Parameters.......................................................................................................... 11

5 Comparison of Capacity Value at High Penetration ....................................................................... 14

5.1 Data Sources.................................................................................................................................. 14

5.2 ReEDS Modeling Assumptions and Parameters............................................................................ 15

5.3 Comparison Results....................................................................................................................... 15

6 Conclusion .......................................................................................................................................... 18

References................................................................................................................................................. 19

Appendix A. ReEDS Temporal Resolution ............................................................................................. 23

Appendix B. ReEDS Geographic Resolution ......................................................................................... 24

Appendix C. WWSIS-2 Balancing Areas................................................................................................. 25
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List of Figures

Figure 1: Mean PV solar capacity factor during summer afternoons (2 – 5pm)................................... 3

Figure 2: Representative solar capacity factor at net peak hour as a function of PV penetration for 

an Arizona BA in August. .................................................................................................................... 4

Figure 3: Representative diurnal net load curve for BA in Arizona for increasing energy fraction 

from PV. The dot marking the peak net load of each curve steadily shifts later into the evening 

as the PV fraction increases................................................................................................................ 4

Figure 4. Discrete temporal representation of solar capacity factor in the ReEDS model ................. 8

Figure 5. Map of ReEDS balancing areas spanning service territory of comparison studies .......... 12

Figure 6. Comparison of solar capacity values in reliability-critical time periods to 

published values................................................................................................................................. 13

Figure 7. State-based solar PV capacity values for reliability-critical time periods for WWSIS-2 

scenarios in 2020................................................................................................................................ 16

Figure 8. Sensitivity of ReEDS PV capacity value to time period and solar energy penetration. .... 17

Figure B-1. Map of ReEDS balancing areas and resource regions (Short 2011)................................ 24

Figure C-1. Map of TEPPC/WWSIS-2 balancing areas .......................................................................... 25

List of Tables

Table 1. Description of Comparison Studies and Results.................................................................... 11

Table A-1. ReEDS Time Period Definitions............................................................................................. 23
1

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1 Introduction

An important emerging issue for electricity system operators is the estimation of renewables’ 

contribution to system adequacy. As supply of electricity must constantly be balanced with 

demand, system operators typically procure a 10%–20% capacity reserve margin to meet 

unplanned outages of existing capacity and unexpected increases in demand (NERC 2013). A 

generator’s ability to help reliably serve load is measured by its capacity value or effective load 

carrying capacity (ELCC)—the firm capacity that a generating unit is able to provide during 

reliability-critical periods. The possibility of outages, whether planned or otherwise, therefore 

necessitates an accurate and dependable method of assessing each unit’s firm capacity 

contribution to planning reserves to avoid loss of load. 

The provision of variable resource renewable energy (VRRE) sources such as wind and solar 

presents a challenge in the assessment of their contributions to planning reserves. Whereas the 

effective capacity value for a conventional thermal generator is well approximated by the 

product of its nameplate capacity and expected forced outage rate (EFOR), variability in solar 

irradiance and wind speeds require a more nuanced approach. Previous studies have estimated 

the capacity value of photovoltaic (PV) solar (Duignan et al. 2012; Madaeni et al. 2013; Perez et 

al. 2006), concentrating solar power (CSP) (Madaeni et al. 2012a), and wind (NERC 2013; 

Keane et al. 2011; Ensslin 2008), finding a wide range of potential capacity values that depend

on technology, resource quality, and correlation of generation and demand, among many factors. 

Numerous techniques can be used to estimate the capacity value of renewable and conventional 

generators, though reliability-based methods are considered to be the most robust and widely

accepted methods (Madaeni et al. 2013). Reliability-based techniques assess how the addition of 

a generator affects the overall reliability of the system, specifically, the likelihood of adequately 

serving load within a planning year. Within this framework, the capacity value of a VRRE 

source is defined as the maximum additional load that the electrical system could serve while 

maintaining the same level of reliability or loss of load expectation (LOLE). The amount of 

additional load that can be served with the addition of the variable generator is its ELCC and is 

equivalent to its capacity value. A drawback of this method, however, is that it requires extensive 

data, including time series spanning several years of load and conventional and renewable 

generation, as well as an inventory of units within a planning area and their respective 

maintenance schedules and forced outage rates.

ELCC-based methods have emerged as an industry-preferred means for assessing the capacity 

value of generating sources (Milligan and Porter 2008a; NERC 2011; Perez et al. 2008), and a 

common practice is to maintain an LOLE of 1 day in 10 years or less. Further discussion of the 

theory and practice of assessing the capacity value of solar have been performed by Duignan et 

al. (2012), Mills and Wiser (2012), and Madaeni et al. (2013), among others.

In contrast to reliability-based methods, approximation methods exist that require more modest 

amounts of system data or that can be performed on generalized systems. Availability of data can 

particularly be a concern for capacity expansion or capacity planning exercises, which typically 

are not resolved at the unit or hourly level, but nevertheless require an estimation of VRRE 

capacity value. One credible method, employed by the Regional Energy Deployment System 

(ReEDS) model in this report, is the Z-method (Dragoon and Dvortsov 2006), which 
2

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approximates LOLE through the distribution of a system’s surplus capacity. We supplement the 

Z-method with a time-period-based method that weighs the relative risk of loss of load within 

each time period.

Utilities and other load-serving entities have historically used a variety of methods to evaluate 

firm solar capacity. These range from detailed LOLP-based reliability evaluations, to time 

period-based estimates of solar capacity factors during top-load periods, and even rules of thumb 

based on engineering judgment (Mills and Wiser 2012). Many utilities do not publically disclose 

their valuation methodology. There is also uncertainty in characterizing changes in solar capacity 

value as a function of energy penetration, as there are very few electricity systems with high 

levels of solar energy penetration to act as case studies. Whatever their method, the assignment 

of capacity credits to VRRE sources is a part of recognizing and evaluating their economic value 

(Borenstein 2008)—and therefore becomes increasingly important for justifying their expanded 

use.

1.1 Report Outline

The purpose of this report is two-fold: first, to compare solar capacity values modeled by the 

ReEDS model to other values published in literature, both at low and high levels of penetration. 

Second, to understand how such factors as resource quality, energy penetration, and coincidence 

of generation and load profile determine the modeled capacity value of utility-scale solar. 

Because contributions to system adequacy increase the value of PV capacity to system operators 

and power producers, a predictive understanding of how capacity value evolves is an important 

prerequisite to understanding PV value.

The remainder of the report is as follows: Section 2 discusses the sensitivity of solar capacity 

value to modeling factors and the implications for other modeling efforts. Section 3 outlines the 

modeling assumptions and operations of the ReEDS model, and Section 4 compares capacity 

value outputs from the ReEDS model to those published by utilities using an ELCC 

methodology. Section 5 compares capacity value outputs from the ReEDS model to those of the 

Renewable Energy Probabilistic Resource Adequacy (REPRA) tool for simulated high levels of 

solar penetration in the Western Interconnection.

2 Factors Influencing Modeled Capacity Value

In this report utility-scale PV capacity value results from the ReEDS model are compared to 

other similar modeling efforts. In doing so, the comparison motivates a broader exploration of 

the nature of capacity value and its calculation, particularly within capacity expansion models. 

This section discusses factors that influence the capacity value calculations—and how these are 

implemented in ReEDS.

2.1 Sensitivity of Capacity Value to Resource Quality

While system operators maintain additional firm capacity beyond expected peak load to hedge 

against unexpected demand or system contingencies, in reality, there are only a few hours of the 

year when system adequacy is a truly pressing concern. The capacity value of a generator is 

assessed based on its ability to serve load during these times, when the LOLP is greatest. Most 

electrical systems in the United States are summer-peaking, due to cooling loads. As a result,

these ‘reliability-critical’ periods typically occur during summer afternoons, though there are 
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Figure 1: Mean PV solar capacity factor during summer afternoons (2 – 5pm)

also electrical systems that experience peak demand in the winter, when electrical demand is 

driven by heating loads. 

Physical location of a solar unit affects the capacity value of a PV unit at a very basic level. 

Namely, there is geographic variation in the annual quantity of solar irradiance as well as the 

diurnal and annual variability in irradiance. Within the ReEDS model, national solar resource is 

represented at the 134 areas that also serve as load balancing areas (BA). These balancing areas 

do not necessarily reflect the actual territories of real-world BAs, or specific reliability rules for 

individual balancing areas. Nevertheless, this level of geographic detail enables the model to 

account for geospatial differences in resource quality (Figure 1)—particularly statistical 

availability during reliability-critical periods.

2.1.1 Correlation of Load and Solar Generation

As a subtler point, geography influences the cooling and heating loads within a balancing area 

(BA), which thereby influences the timing of high LOLP hours. The key issue is to understand 

the degree of correlation between a solar unit’s availability and periods of high LOLP. In 

general, the correlation of load and solar generation varies enough between BA to warrant 

detailed investigation.

2.2 Solar Energy Penetration

Solar PV capacity value is also known to be highly sensitive to increasing levels of PV 

deployment within the planning region (Perez et al. 2006; Lew et al 2010; Mills & Wiser 2012; 

Madaeni et al. 2012b; Olson & Jones 2012). PV capacity value is mainly driven by its generation 

level during the most critical hours of the year, when load is most likely to be dropped due to 

outages or available capacity. Typically, these periods of time are found during the early 

evenings of a few weeks of the year, especially for summer-peaking systems. When deployment
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of PV is at low levels of energy penetration, the additional PV generation does not significantly 

affect timing of reliability-critical hours. However, since the profile of solar generation is largely 

coincident with a summer-peaking utility’s load profile, increasing levels of solar generation 

shifts the critical hours to later hours, when solar irradiance is lower as the sun is setting, 

decreasing PV capacity value. At high levels of penetration, when net load has been shifted 2 - 3 

hours, the capacity factor reaches near-zero levels—as irradiance during the evening is 

negligible. The most critical hours are typically those with highest levels of net load, i.e., load 

minus variable generation.

To better illustrate the sensitivity of solar capacity value to energy penetration, the capacity 

factor is modeled for a representative solar unit in the ReEDS ‘p28’ BA, which overlaps with 

territory served by the Arizona Public Service utility in central Arizona. Demand in this BA is

summer-peaking and the top load hours typically occur during late August afternoons. Solar 

capacity factors were calculated for units located in Flagstaff, Arizona, using NREL’s System 

Advisor Model (SAM) 1 using the mean August diurnal generation profile.

2 The SAM model 

has a specific PV module and an hourly simulation engine. With the appropriate solar resource 

data, it is used to develop capacity factors by time-slice for each ReEDS region. For this 

illustration, wind contribution is assumed to be negligible.

Figure 2: Representative diurnal net load curve 

for BA in Arizona for increasing energy fraction 

from PV. The dot marking the peak net load of 

each curve steadily shifts later into the evening 

as the PV fraction increases.

Figure 3: Representative solar capacity factor 

at net peak hour as a function of PV penetration 

for an Arizona BA in August.

 1 See https://sam.nrel.gov/ for more details 2 Note that this result is intended only to illustrate the functional form of the relationship between capacity value and 

penetration and the exact quantities calculated should not be interpreted literally.
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As levels of annual solar energy penetration increase from 0% to 20%, the peak load in the 

diurnal load profile is reduced and shifted to later in the day (Figures 2 and 3). The capacity 

factor at the point of peak net load erodes following an exponential form and, as predicted, 

becomes negligible at high levels of annual energy penetration. 

3 ReEDS Background

The ReEDS model is a generation and transmission capacity expansion model of the electricity 

system of the contiguous United States. Developed by the National Renewable Energy 

Laboratory (NREL), it has been used for a number of projects exploring possible evolution of the 

U.S. electricity system and evaluating the potential for and impact of growth in renewable energy 

technologies, including the recent SunShot Vision (EERE 2012) and Renewable Electricity 

Futures studies (NREL 2012). ReEDS is a linear program that chooses investment and operation 

decisions to serve load and meet system requirements at the least overall system cost. Operating 

sequentially along 2-year periods, ReEDS develops scenarios of electric sector evolution from 

2010 to 2050. Modeling assumptions and parameters key to this investigation are briefly 

described; a more thorough documentation of the ReEDS model, however, has been conducted 

by Short et al. (2011).

3.1 Model Structure

ReEDS uses a number of assumptions to forecast capacity expansion from 2010 to 2050. The 

following technology and cost assumptions were used in this analysis:

• Load: Ventyx Velocity Suite (2010) regional hourly load profiles, scaled annually by 

expected regional load growth (EIA 2013)

• Technology Costs: Annual Energy Outlook (EIA 2013) projections in 5-year increments

• Existing Fleet and Retirements: A combination of Ventyx (2010) existing fleet data and 

planned and announced retirements; retirements of coal units are supplemented by data 

from M.J. Bradley & Associates (Saha 2013)

• Policy: All publically announced federal and state renewable incentives, including 

federal investment tax credits, production tax credits, and state Renewable Portfolio 

Standards and solar carve outs.

The ReEDS model is especially focused on representing renewable energy technologies in 

capacity expansion decisions. To best represent such decisions, parameters that drive variation in 

the siting and integration costs of solar and wind generating technologies are emphasized. In 

particular, the model uses a high level of spatial resolution—where wind and CSP resources are 

defined at 356 resource regions and solar PV at the 134 regions that also serve as load BAs. Each 

resource is regionally characterized by a set of supply curves—constructed from NREL resource 

assessments (Lopez et al. 2012)—that distinguish resource quality and the cost of accessing the 

local transmission network. This level of geographic detail enables the model to account for 

geospatial differences in resource quality, transmission needs, electrical (grid-related) 

boundaries, political and jurisdictional boundaries, and demographic distributions. The 134 load 
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regions are connected by an aggregated transmission network that gives ReEDS the ability to 

discern the relative value of development sites across regions. 

ReEDS dispatches generation for 17 time-slices (4 time-slices for each season representing 

morning, afternoon, evening, and nighttime, with an additional summer-peak time-slice)

(Appendix A). The temporal detail enables ReEDS to consider both seasonal and diurnal changes 

in demand and resource availability—but limits its ability to account for hour-on-hour variations. 

To account for demand and resource variability within each time-slice, ReEDS uses statistical 

calculations to estimate BA reliability needs and contributions from VRRE sources. In addition 

to the capacity value metric that is the focus of this paper, ReEDS also estimates induced 

operating reserve requirements and curtailment of excess production from VRRE sources.

For new investments, ReEDS can choose from a broad portfolio of conventional generation, 

renewable generation, storage, and demand-side technologies. Plants provide power to meet 

load, capacity toward adequacy requirements, and operating (spinning or non-spinning) reserves.

Conventional generators contribute their nameplate capacity toward adequacy requirements and 

supply operating reserves while variable renewables contribute their calculated capacity value 

and require additional operating reserves. 

Three solar PV system types are modeled—utility-scale (UPV), distributed utility-scale (DUPV), 

and distributed rooftop. UPV and DUPV are interconnected to the grid at the transmission level 

and are assumed to be utility controlled, whereas distributed rooftop is connected at the 

distribution network level, behind the meter. Rooftop PV projections are developed outside of 

ReEDS, in NREL’s SolarDS model (Denholm et al. 2009) because decisions on rooftop 

installations are assumed to be made on a different basis (i.e., by individuals) than centralized 

utility or power-producer decisions. The differences in ReEDS between UPV and DUPV are 

primarily about size and siting freedom: DUPV systems are smaller and are assumed to be close 

to load, while UPV systems are wide-ranging. This report exclusively applies to UPV and does 

not analyze capacity value for DUPV and rooftop PV systems.

UPV represents single-axis tracking PV systems with a unit size of 100 MW. Performance 

characteristics for central PV were developed by the SAM PV module (NREL 2010a) using 

annual hourly weather files from the National Solar Radiation Database (NSRDB 2010) for 939 

sites throughout the contiguous United States from 1998 to 2005. The site with the highest 

average annual PV capacity factor in each BA was used to represent the performance (i.e., 

capacity factor in each time-slice) of central PV capacity installed in that BA. For each site, 

generation profiles were averaged across the 8-year time period. PV capacity factors represent 

the average AC capacity factor after taking into account the AC-DC conversion (using an 82%

derating factor). All other power metrics (e.g., nameplate capacity and capacity value) are stated 

in terms of their derated AC power output.

The ReEDS transmission network is a 134-node system connected by roughly 300 transmission 

corridors representing the collection of real transmission lines that cross BA boundaries and are 

characterized by the carrying capacity of those lines. The transmission network is divided into 

three asynchronous interconnects (West, East, ERCOT) by a set of AC-DC-AC interties. 

Transmission flows across the system are determined by a linearized DC power flow 

approximation, a standard method for representing power flows in electricity system models, 
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described and evaluated in Stott et al. (2009). The transmission network allows BAs to share 

power and ancillary services with each other, buffering each other’s needs. It also permits longdistance transmission of remote renewable resources from high-resource areas to major loads.

ReEDS uses the net power flows within each time-slice to accurately account for sources of 

generation. Exporting regions are assumed to share generators’ electricity proportionally across 

all outgoing lines. This proportional sharing assumption, introduced by Bialek (1996), links 

ownership between each source and load: which loads each generator has served and in what 

proportion. Generation is permitted to be exported and thus serve load outside the source BA. 

Variability parameters (e.g., capacity value and curtailments) are characterized based on the 

destinations of generated power, but accrue at the source. In the configuration of ReEDS used for 

this analysis, all generators share their output proportionally with power flows. There is no 

accounting for bilateral contracts in which a remote renewable resource would be dedicated to 

serving a particular load.

3.2 Capacity Value Calculations

ReEDS uses a measure of a VRRE generator’s ELCC to determine its contributions to planning 

reserves in each of the 17 time periods. That is, adequacy/reliability is defined in terms of the 

likelihood that the system (BA, transmission zone, service territory) will have insufficient 

available generating capacity to meet load during a given period. We use the Z-method algorithm 

(Dragoon and Dvortsov 2006; Madaeni et al. 2013) to approximate a VRRE source’s ELCC. 

This method assumes that, because of the large number of generating units in an electrical 

system, the distribution of hourly surplus capacity has a Gaussian form. The Z-statistic of the 

surplus capacity distribution, the ratio of the mean surplus to standard deviation, is a 

representation of the statistical likelihood of experiencing a loss of load. Keeping the Z-statistic 

constant between systems with PV and without approximates keeping a constant LOLP for each 

period—and an ELCC estimate can be derived from these assumptions. For each BA, ReEDS 

computes a bulk capacity value for all existing VRRE units, as well as an estimate for the 

marginal capacity value of potential VRRE investments in the next solve period.

The Z-method is used by ReEDS to estimate capacity value because it permits the approximation 

of capacity value without conducting an hourly time-series analysis, which is infeasible given 

ReEDS’s temporal resolution. However, the Z-method assumption of a Gaussian form can be 

violated under high-renewable scenarios if the real time-slice probability distribution of VRRE 

output does not follow a Gaussian distribution.

3.2.1 Capacity Value Point Estimates

System planners typically determine the capacity value of a generator as a point value that 

represents the unit’s ability to reliably serve load over the course of a planning year. This point 

value is the result, however, of analyzing hourly-level LOLPs. Hourly-level analysis is important 

because of differences in the availability of a solar unit. However, because the ReEDS model is 

resolved over 17 time-slices, these inter-hourly differences are difficult to model. 

Figure 4, which shows the mean summer (June–August) diurnal capacity factor for a 

representative solar unit in Flagstaff, Arizona, illustrates the temporal discreteness in the ReEDS 

model. Overlaid in the figure are the average capacity factors for the Flagstaff solar unit 
8

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discussed earlier during three select ReEDS time periods (summer morning, summer afternoon, 

and summer evening). Collectively, these three periods span the most critical load hours for the 

BA. As solar penetration increases, the peak net load period shifts from afternoon to evening, 

and the corresponding capacity factor in the residual peak time-slice—the most important factor 

in estimating capacity value—drops as a step function.

Figure 4. Discrete temporal representation of solar capacity factor in the ReEDS model

ReEDS mitigates the issue of steep time-slice gradients via two strategies. Internally, the ReEDS 

model does not employ a single point estimate of capacity value across time periods, but rather 

uses a capacity value for each time period that is based on the average capacity factor for hours 

spanning that time period. By varying the value of capacity available during each ReEDS time 

periods, this mimics the time-varying availability of actual solar units. 

Second, a planning reserve constraint (1) inherently provides the optimization with information 

about the relative difficulty of serving load in each ReEDS time period as solar penetration 
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increases. For each time-slice (m) and BA (n), available capacity must exceed the planning 

reserve target: 

�CONVnm + �VARnm ≥ (1 + r) ∙ �Pnm

n,m n,m

(1)

n,m

Where CONVnm is the available conventional capacity (including forced outage rates) in period 

m and BA n, VARnm is the available variable capacity—that is, the product of nameplate capacity 

(MW) and capacity credit (fraction), r is the planning reserve margin (fraction), and P is the 

expected peak time-slice load. When variable capacity is low, the planning reserve constraint is 

most binding for the peak load hour—likely, the summer afternoon when solar capacity value is 

high. As solar capacity increases, however, the relative difficulty of meeting the planning reserve 

target shifts from summer afternoon, when there is already sufficient available solar capacity, to 

evening when capacity factors are lower. In other words, when making future capacity expansion 

decisions at high solar penetration, ReEDS recognizes the decreased value of solar capacity 

services and makes optimal investment decisions relative to other expansion options. 

One more feature is needed to quantify the relative difficulty of meeting planning reserve targets, 

as well as scenarios in which the planning reserve constraint is binding in more than one period.

When available capacity is scarce enough that the planning reserve constraint is binding, the 

marginal price (shadow price) on the constraint represents the additional cost the system would 

incur to increase reserve capacity by a single unit. That is, the marginal price on the planning 

reserve constraint signals the relative difficulty of serving load in each period and can be used to 

appropriately weight the capacity value in that period. As solar penetration increases, the ReEDS 

planning reserve constraint will be increasingly binding in evening periods.

3.2.2 Benefits of Power Diversification

Power flow assumptions in ReEDS affect capacity value calculations, where the diversification 

of power flow across multiple BAs tends to increase solar PV capacity value. By sourcing PV 

from multiple, diverse locations, a load region can narrow its PV production probability 

distribution and reduce the integration burden of those resources. This encourages investment in

areas that will raise the level of diversification seen at each local load and thereby helps to slow 

the erosion of capacity value as penetration levels increase. 
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4 Comparison of Capacity Value at Low Penetration

Between planning areas, there exists considerable variation in the capacity credit assigned to a 

UPV unit based on its geographic location, the utility’s load profile, existing level of PV 

deployment, and the method used to assess capacity value. In this section the ReEDS model’s

estimates of capacity value are compared to those published by utilities or other research teams 

at low levels of solar energy penetration—that is, for actual electrical systems with specified 

levels of PV deployment or with low (simulated) levels of PV penetration. Comparison is 

restricted to studies conducted using an ELCC-based methodology. 

4.1 Estimates of Solar Capacity Credit in Planning Studies and 

Similar Literature

The particular method used by electricity system planners to estimate solar capacity value 

substantially affects the calculation of capacity value, and thus the value awarded. Use of an 

ELCC-based method is preferable because of the acknowledgment of inter-hour variability in the 

unit’s generation, particularly during hours when the electrical system is expected to have a 

higher LOLP (Perez et al. 2008a). To benchmark the ReEDS model, we compiled a set of solar 

capacity value studies conducted for known systems based only on ELCC methods (Table 1).

Though an ELCC-based method has not been fully adopted by all utilities in their planning 

studies, three utilities, Arizona Public Service (APS), Public Service of Colorado (PSCo), and 

TriState Generation and Transmission (TriState), were identified to employ an ELCC/LOLP 

framework in their reliability and planning studies (APS 2013; PSCo 2013; TriState 2010). Other 

researchers not explicitly associated with a utility have also assessed solar capacity value for 

known non-test electrical systems (Lu et al 2012; Perez et al. 2008a; Perez et al. 2008b). These 

studies correspond, respectively, to the Nevada Energy, Nevada Power, Portland General 

Electric utilities, and territory served by the New York Independent System Operator (ISO). 

While many of the studies report a single point estimate of capacity values, others report a range 

of values. The range in reported capacity value could be due to assessing the capacity value for a 

variety of sites within the planning area as well as variation in their scenario parameters. 
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This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Table 1. Description of Comparison Studies and Results

Utility District 

Studied

(Authors)

Summary of Methodology Reported 

Capacity value

Arizona Public 

Service 

(APS 2013)

Performance data from installed system in service territory, load 

profiles from 2003 to 2007; single-axis tracking; deployment

projections for 2015; ELCC simulations for existing capacity and 

next 100 MW built

45.9%–48.4% 

Nevada Energy

(Lu et al. 2012)

Nevada Energy southern system generation fleet in the 2007 

study year; ELCC calculation using LOLE of 1 day in 10 years 57.4%

Nevada Power

(Perez et al.

2008a)

Satellite-derived resource data to simulate output; simulated 2% 

PV deployment; 30° SW-facing fixed systems; ELCC calculation 71%

New York ISO

(Perez et al.

2009b)

South-facing fixed slope; ELCC calculation for simulated 2% PV 

grid penetration using 2007 generation and load data 44.3–78.3%

Portland General 

Electric 

(Perez et al.

2008a)

Satellite-derived resource data to simulate output; simulated 1% 

PV deployment; 30° SW-facing fixed systems; ELCC calculation 31%

Public Service 

Colorado 

(Xcel 2013)

2009-2010 historic load and solar generation; single-axis 

tracking; ELCC calculation using LOLE of 1 day in 10 years 41%–47%

TriState 

(TriState 2010)

LOLP method, with expected capacity availability during peak 

load hour; unclear assumptions for generation and load data 20%–57%

4.2 ReEDS Scenario Parameters

ReEDS calculations of solar capacity value were compared to the studies in Table 1 in order to 

benchmark performance of the model. To facilitate an equitable comparison, scenarios were 

constructed to match each utility region’s geographic location, existing generation fleet, and PV 

deployment levels as closely as possible. By default, ReEDS uses historic capacity expansion 

from 2010 to 2013 and business-as-usual assumptions for capacity expansion projections 

thereafter. Operation of the fleet is made in a least-cost optimization framework. For studies 

based on a specific forecasted level of PV penetration, the ReEDS model is required to exactly 

attain the specified level of PV deployment at the least-cost solution. 

Because ReEDS balancing area service territories do not exactly match the service territory of 

each of the comparison studies, capacity value is geographically compared using the smallest set 

of ReEDS BAs that wholly encapsulates each study’s service territory (Figure 5). If the study 

territory encapsulates several ReEDS BAs, the range of capacity values among BAs within the 

study territory are reported. See B-1 for a map of the BA regions. 
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Figure 5. Map of ReEDS balancing areas spanning service territory of comparison studies

The ReEDS model does not report annual point estimates of capacity value but rather a capacity 

value for each of the model’s 17 time periods (Appendix A)—and thus transitions between time 

periods are abrupt. Solar capacity value in each time period is primarily determined by the mean 

capacity factor for hours in that time period. In practice this means that while an hourly ELCC 

evaluation would be expected to see a smooth transition from afternoon to evening, ReEDS 

observes two distinct regimes—afternoon and evening—and an abrupt shift between them.

While ReEDS reports capacity values in this stepwise manner, the information loss at the timeslice interface is mitigated by ReEDS’ simultaneous consideration of adequacy in all time-slices. 

In particular, as the reliability-critical period shifts from afternoon to evening, ReEDS can be 

thought of as blending the two capacity values for the afternoon and evening time-slices. 

Because planning reserves are required to be met in all time periods with a time-varying capacity 

value, this simulates a utility’s requirement of minimizing the LOLE over all service hours.

Figure 5 compares the capacity values reported by utilities to results from the ReEDS model. For 

each utility, we use capacity value for the set of ReEDS time periods spanning that utility’s 

reliability-critical periods. Comparisons might include more than one BA if the utility has 

territory spanning more than one ReEDS BA. For the areas considered, these time periods are 

mostly the “summer afternoon” and “summer evening” periods, although there are some regions 

considered that are winter-peaking. This method assumes that LOLP is well-correlated with net 

system load. In particular, Madaeni et al. (2013) showed that weighing a solar generation unit’s 

capacity factor by the LOLP for the 10 highest net load hours provided an accurate estimate of 
13

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the ELCC. That is, due to strong correlation between load and generation, the capacity value is 

well-estimated by these few, most reliability-critical hours of the year. 

For example, ReEDS models the APS utility with four BAs (p27–30). For 3 of the APS BAs, 

their 10 highest load hours occur in both the summer afternoon period as well as the summer 

evening; the fourth highest load hours solely occur during the summer evening time period 

(Figure 5). The APS study reports bulk capacity values of 45.9%–48.4% for 242–166 MW of 

(modeled) capacity in 2015. In contrast, results from ReEDS reports an average bulk capacity 

value of 54.9% in summer afternoon and 14.4% in summer evening for the same levels of 

penetration in 2015. 

Figure 6. Comparison of solar capacity values in reliability-critical time periods to 

published values

Results from the comparison show that the ReEDS modeled capacity values for reliabilitycritical time periods mostly bound the reported capacity values. Two exceptions are for the 

Nevada Power and New York ISO studies, which report somewhat greater capacity values than 

those calculated by ReEDS. Notice among the ReEDS reporting that time-slices produce clusters 

of estimates and that summer afternoon capacity value clusters are substantially higher than 

summer evening clusters as predicted by the capacity factor analysis above. Interpreted in that 

light, the external sources are undergoing a transition from afternoon importance to evening 
14

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importance, and, in fact—in particular Xcel, APS, and NV Energy, being close to the summer 

afternoon cluster—are early in that transition. For the majority of studies compared (Xcel, APS, 

Tri-State, NV Energy), capacity value in the summer afternoon period slightly over-predicts the 

reported capacity value. This bias is explained when considering the load hours represented by 

each time period. The APS grid, for example, has historically achieved its annual peak load 

between 4 pm and 5 pm on summer weekdays (R.W. Beck 2009). Capacity values for the APS 

system, then, should be intermediate to those of the summer afternoon and summer evening time 

periods but closer to the summer afternoon capacity value—the result observed. A similar logic 

applies to the remaining study regions.

5 Comparison of Capacity Value at High Penetration

Several researchers have conducted modeling efforts to quantify the operational value of solar 

and other VRRE generation at high (10%+) levels of penetration (Perez et al. 2006; Lew et al.

2010; Mills and Wiser 2012; Madaeni et al. 2012b; Olson and Jones 2012). These studies find 

that the capacity credit assigned to solar generation declines significantly at high level of energy 

penetration for the reasons outlined in Section 1.2. As penetration increases, the marginal 

economic value of PV drops considerably, primarily because of changes in capacity value, but 

also in energy value (Mills and Wiser 2012). Clearly, this decrease in value decreases the overall 

economics of future solar units (Olson and Jones 2012) and could suppress additional 

investment. 

Unfortunately, there are very few actual electrical systems operating at high levels of solar 

penetration, and so there is scarce available literature on the capacity value of solar on real 

electrical systems. Therefore, the ReEDS model’s treatment of solar capacity value at high levels 

of energy penetration is compared with results derived from Phase 2 of the Western Wind and 

Solar Integration Study (WWSIS-2) (Lew et al. 2013). The WWSIS-2 sought to simulate grid 

operation in the U.S. Western Interconnection for four hypothetical high-renewable deployment 

scenarios in 2020. Capacity values for the WWSIS-2 scenarios are calculated using NREL’s 

Renewable Energy Probability Resource Adequacy tool (REPRA) (Ibanez and Milligan 2012), 

which estimates the capacity value of VRRE sources using a time series ELCC algorithm.

5.1 Data Sources

Representation of the generation fleet for the REPRA tool is based on Phase 2 of NREL’s 

WWSIS (Lew et al. 2013). This data is consistent with studies performed by the Western 

Electricity Coordinating Council’s (WECC’s) TEPPC. The WWSIS-2 studied the performance 

of the power system in the Western Interconnection under high levels of wind and solar energy 

penetration. A reference scenario was created based on WECC’s TEPPC (WECC 2009) with 

wind and solar (PV and CSP) penetration at 9.5% and 3.5%, respectively. Three high penetration 

scenarios were also defined: high wind (25% wind, 8% solar), high solar (25% solar, 8% wind),

and high mix (16.5% of wind, 16.5% solar). The ReEDS model was used to inform capacity 

expansion for the WWSIS-2 scenarios, and the commercial production simulation tool PLEXOS 

is used to model unit commitment (Lew et al. 2013).

Load time series data from 2006 was chosen from the Ventyx Velocity Suite (Ventyx 2010) and 

was forecasted based on load growth projections to represent load in 2020. The wind dataset was 

derived from the large wind speed and power database developed by 3TIER using a numerical 
15

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weather prediction (NWP) model applied to the West (3TIER 2010). Because the model allows 

for the simulation of the weather, at any time and space, wind speed data was sampled at 

representative hub heights for modern wind turbines every 10 minutes for a 3-year period on a 2-

km spatial resolution. The resulting dataset was then used to construct the 2006 time series, 

which was paired with the 2006 load data time series to preserve the consistency of common 

weather impacts. Solar data was produced by NREL (Orwig et al. 2011) based on the satellitederived irradiance generated by the State University of New York/Clean Power Research 

(Wilcox et al. 2007), which is available on a 10-km grid at an hourly resolution. 

5.2 ReEDS Modeling Assumptions and Parameters

As in Section 3, to facilitate equitable comparison of the REPRA and ReEDS models, scenario 

parameters for the ReEDS model were chosen to parallel those of the WWSIS-2 scenarios. These 

include levels of solar PV and wind deployment and geographic region of comparison. Two 

differences remain:

• Capacity Expansion: The ReEDS scenario is prescribed to match the gross WECC-wide 

PV deployment levels for the four WWSIS-2 scenarios by 2020, and the ReEDS model 

was used to inform capacity expansion decisions for both analyses. However, because 

each analysis uses different model versions and assumptions, the geographic distribution 

of renewable and conventional capacity deployment within the ReEDS and WWSIS-2

analyses may differ. For similar reasons, generation is not harmonized between the 

models.

• Balancing Area Regions: Both the ReEDS model and REPRA tool use slightly different 

BA definitions for the Western Interconnection. Appendix B and Appendix C show 

boundaries for each model’s BAs. For geographic equity, results from the two models are 

compared at a state level; when a BA overlies multiple states it is allocated to whichever 

state contains the majority of its area. 

5.3 Comparison Results

As in Section 3.3 the ReEDS solar capacity value is reported as the range of capacity values 

during the BA’s reliability-critical time-slices. Figure 7 shows the range of ReEDS capacity 

values for the ReEDS time periods that contain each BA’s 10 highest net load hours. For the 

areas considered for comparison3

, these time periods are the summer afternoon, summer 

evening, and winter afternoon time-slices. For the majority of ReEDS BAs, summer afternoon 

and summer evening are the most reliability-critical time-slices. An exception is Montana, a 

winter-peaking system, and so adequacy concerns are greatest during the winter afternoon. Each 

point within Figure 7 represents the capacity value for the ReEDS or REPRA model within a 

single BA for a given time period and WWSIS-2 scenario. That is, the variation within a subplot 

at a given penetration level reflects variation in capacity value between different BAs in the same 

state. All four WWSIS-2 scenarios are shown in the plot to demonstrate the relationship between 

capacity value and penetration.

 3 Note that the states of Idaho and Washington as well as the El Paso area of Texas are regions within the Western 

Interconnection. However, because an insubstantial amount of solar capacity was built for these regions in each 

model, results for those regions were excluded from this analysis.
16

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Figure 7. State-based solar PV capacity values for reliability-critical time periods for WWSIS-2

scenarios in 2020

The range of ReEDS capacity values bounds the REPRA values in most states (Arizona, 

California, Colorado, New Mexico, Nevada, Utah) but is a poor fit in states with few data points 

for comparison. While there is disagreement between ReEDS and REPRA at low penetration 

levels in Arizona, Colorado, and New Mexico, agreement improves at high penetrations. Erosion 

within a ReEDS time slice is generally shallower than that of the REPRA results, which is 

consistent again with the set of reliability-critical hours shifting into the evening as penetration 

increases. The within-time-slice ReEDS results, of course, do not include that transition, but 

recall that ReEDS itself does so implicitly by requiring all systems to meet adequacy needs in all 

time-slices.

Notice, also, that there is some erosion of capacity value within a time-slice as penetration 

increases. This is consistent with the hypothesis that within any set region adding more PV 
17

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increases its self-correlation. As does a system operator, ReEDS has the capability to diversify its 

resource base somewhat, but not fully, and the intra-time-slice erosion represents the limit of 

that ability.

Figure 8 shows the bulk capacity credit from the WWSIS-2 results for all ReEDS daytime timeslices, not just reliability-critical periods. That is, each subplot aggregates results from the four 

WWSIS-2 scenarios (3.5%, 8%, 16.5%, and 25% solar penetration WECC-wide) and for the 33 

ReEDS balancing areas used to represent WECC. Results suggest that a large source of capacity 

value variation within the ReEDS model is between time-slices. We suggest that capacity value 

erosion within a time period is explained through increased self-correlation of energy production, 

as well as decreases in available high-quality resource sites within the region. This is because 

shifts in peak net load are not explicitly considered within a time period. Variation in modeled 

capacity value holding penetration constant can be explained through geographic variation in 

resource quality in Western BAs—though this is not formally shown.

Figure 8. Sensitivity of ReEDS PV capacity value to time period and solar energy penetration.
18

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6 Conclusion

ReEDS was designed to represent characteristics that drive variation in investment and operation 

costs of renewable energy technologies, including geospatial resource assessment and integration 

of variable resources into a reliable electricity grid. Because these characteristics give the model 

accurate information about the economic value of, for instance, an additional unit of solar 

capacity, ReEDS is able to make well-informed investment decisions. Capacity value, as 

discussed here, is one of the economic components ReEDS includes in its decision making—one 

that can change dramatically with system configuration and is important to model dynamically. 

To accurately reflect solar capacity value in capacity expansion decisions, ReEDS models a 

number of factors that determine its ELCC. These include representation of the statistical 

availability of a solar unit, a high level of geographic resolution in resource quality and grid 

conditions, and correlation of residual load and solar generation. Additionally, ReEDS 

simultaneously considers adequacy issues in all time-slices. Because the value of capacity 

services is highest during reliability-critical periods, and increased solar generation shifts those 

periods away from peak solar output, this accounts for the diminishing capacity value of solar at 

high levels of penetration. We find that capacity value outcomes from the ReEDS model 

compare favorably with results from hourly resolution ELCC-based analyses for a range of real 

and modeled levels of solar energy penetration. 
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Xcel Energy Services, Inc. (May 2013). “Costs and Benefits of Distributed Solar Generation on 

the Public Service Company of Colorado System.”
23

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Appendix A. ReEDS Temporal Resolution

The ReEDS model dispatches generation for 17 time-slices (4 time-slices for each season 

representing morning, afternoon, evening, and nighttime, with an additional summer-peak timeslice). This level of temporal detail enables ReEDS to consider seasonal and diurnal changes in 

demand and resource availability but limits its resolution at inter-hour analysis. The planning 

reserve constraint that maintains system adequacy is held at each of the 16 standard time-slices. 

For adequacy purposes, the superpeak is assumed to be a subset of the summer afternoon (H3) 

time-slice.

Table A-1. ReEDS Time Period Definitions

Name 

Hours 

Per 

Year 

Season Time of 

Day Time Period 

H1 736 Summer Night 10 p.m. to 6 a.m. 

H2 644 Summer Morning 6 a.m. to 1 p.m. 

H3 328 Summer Afternoon 1 p.m. to 5 p.m. 

H4 460 Summer Evening 5 p.m. to 10 p.m. 

H5 488 Fall Night 10 p.m. to 6 a.m. 

H6 427 Fall Morning 6 a.m. to 1 p.m. 

H7 244 Fall Afternoon 1 p.m. to 5 p.m. 

H8 305 Fall Evening 5 p.m. to 10 p.m. 

H9 960 Winter Night 10 p.m. to 6 a.m. 

H10 840 Winter Morning 6 a.m. to 1 p.m. 

H11 480 Winter Afternoon 1 p.m. to 5 p.m. 

H12 600 Winter Evening 5 p.m. to 10 p.m. 

H13 736 Spring Night 10 p.m. to 6 a.m. 

H14 644 Spring Morning 6 a.m. to 1 p.m. 

H15 368 Spring Afternoon 1 p.m. to 5 p.m. 

H16 460 Spring Evening 5 p.m. to 10 p.m. 

H17 40 Summer Peak 40 highest demand hours of 

summer
24

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Appendix B. ReEDS Geographic Resolution

ReEDS represents the continental United States using 134 BAs, the regional level at which 

demand requirements must be satisfied and all non-wind/CSP technology expansion occurs. 

Portions of this report’s analysis only pertain to the Western Interconnection, which has 35 BAs. 

Because BA service territories do not exactly match the service territory of the comparison 

studies in Section 3 or the WWSIS-2 balancing areas, for the purpose of comparison, we use the 

smallest set of ReEDS BAs that wholly encapsulates each study’s service territory. If the study

territory encapsulates several ReEDS BAs, we report the range of capacity values for each BA

within the study territory.

Figure B-1. Map of ReEDS balancing areas and resource regions (Short 2011)
25

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Appendix C. WWSIS-2 Balancing Areas

The WWSIS-2 represents the U.S. Western Interconnection using 36 BAs (Figure C-1) 

designated by the WECC’s TEPPC (TEPPC 2009). This data is consistent with other TEPPC 

studies except that WECC-2 BAs in Canada and Mexico are excluded. Because WWSIS-2 BA 

service territories do not exactly match the service territories of BAs used in ReEDS, for the 

purpose of comparison we compare the two models at a state-level; when a BA overlies multiple 

states it is allocated to whichever state contains the majority of its area. 

Figure C-1. Map of TEPPC/WWSIS-2 balancing areas